Does your site rank for other things besides the keywords you are targeting?
For instance: Does your site rank for the exact title of the home page?
Does it rank if you copy a unique sentence of text from the homepage and search for that?
Is the home page still getting referrals from google as a landing page for OTHER keywords?
Does your home page show up in the results if you use plural / very close semantically related keywords?
Does it rank if you use your keyword AND the name of the town where your business is (e.g., "widgets london"), or some other word that appears on your home page?
For example, lots of sites say things like: "We traverse the globe to bring you the best widgets from the around the world"
so maybe search for "traverse widgets" or something like that.